/*
 *      bignumber.js v6.0.0
 *      A JavaScript library for arbitrary-precision arithmetic.
 *      https://github.com/MikeMcl/bignumber.js
 *      Copyright (c) 2018 Michael Mclaughlin <M8ch88l@gmail.com>
 *      MIT Licensed.
 *
 *      BigNumber.prototype methods     |  BigNumber methods
 *                                      |
 *      absoluteValue            abs    |  clone
 *      comparedTo                      |  config               set
 *      decimalPlaces            dp     |      DECIMAL_PLACES
 *      dividedBy                div    |      ROUNDING_MODE
 *      dividedToIntegerBy       idiv   |      EXPONENTIAL_AT
 *      exponentiatedBy          pow    |      RANGE
 *      integerValue                    |      CRYPTO
 *      isEqualTo                eq     |      MODULO_MODE
 *      isFinite                        |      POW_PRECISION
 *      isGreaterThan            gt     |      FORMAT
 *      isGreaterThanOrEqualTo   gte    |      ALPHABET
 *      isInteger                       |  isBigNumber
 *      isLessThan               lt     |  maximum              max
 *      isLessThanOrEqualTo      lte    |  minimum              min
 *      isNaN                           |  random
 *      isNegative                      |
 *      isPositive                      |
 *      isZero                          |
 *      minus                           |
 *      modulo                   mod    |
 *      multipliedBy             times  |
 *      negated                         |
 *      plus                            |
 *      precision                sd     |
 *      shiftedBy                       |
 *      squareRoot               sqrt   |
 *      toExponential                   |
 *      toFixed                         |
 *      toFormat                        |
 *      toFraction                      |
 *      toJSON                          |
 *      toNumber                        |
 *      toPrecision                     |
 *      toString                        |
 *      valueOf                         |
 *
 */


var BigNumber,
    isNumeric = /^-?(?:\d+(?:\.\d*)?|\.\d+)(?:e[+-]?\d+)?$/i,

    mathceil = Math.ceil,
    mathfloor = Math.floor,

    bignumberError = '[BigNumber Error] ',
    tooManyDigits = bignumberError + 'Number primitive has more than 15 significant digits: ',

    BASE = 1e14,
    LOG_BASE = 14,
    MAX_SAFE_INTEGER = 0x1fffffffffffff,         // 2^53 - 1
    // MAX_INT32 = 0x7fffffff,                   // 2^31 - 1
    POWS_TEN = [1, 10, 100, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13],
    SQRT_BASE = 1e7,

    // EDITABLE
    // The limit on the value of DECIMAL_PLACES, TO_EXP_NEG, TO_EXP_POS, MIN_EXP, MAX_EXP, and
    // the arguments to toExponential, toFixed, toFormat, and toPrecision.
    MAX = 1E9;                                   // 0 to MAX_INT32


/*
 * Create and return a BigNumber constructor.
 */
function clone(configObject) {
    var div, convertBase, parseNumeric,
        P = BigNumber.prototype,
        ONE = new BigNumber(1),


        //----------------------------- EDITABLE CONFIG DEFAULTS -------------------------------


        // The default values below must be integers within the inclusive ranges stated.
        // The values can also be changed at run-time using BigNumber.set.

        // The maximum number of decimal places for operations involving division.
        DECIMAL_PLACES = 20,                     // 0 to MAX

        // The rounding mode used when rounding to the above decimal places, and when using
        // toExponential, toFixed, toFormat and toPrecision, and round (default value).
        // UP         0 Away from zero.
        // DOWN       1 Towards zero.
        // CEIL       2 Towards +Infinity.
        // FLOOR      3 Towards -Infinity.
        // HALF_UP    4 Towards nearest neighbour. If equidistant, up.
        // HALF_DOWN  5 Towards nearest neighbour. If equidistant, down.
        // HALF_EVEN  6 Towards nearest neighbour. If equidistant, towards even neighbour.
        // HALF_CEIL  7 Towards nearest neighbour. If equidistant, towards +Infinity.
        // HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.
        ROUNDING_MODE = 4,                       // 0 to 8

        // EXPONENTIAL_AT : [TO_EXP_NEG , TO_EXP_POS]

        // The exponent value at and beneath which toString returns exponential notation.
        // Number type: -7
        TO_EXP_NEG = -7,                         // 0 to -MAX

        // The exponent value at and above which toString returns exponential notation.
        // Number type: 21
        TO_EXP_POS = 21,                         // 0 to MAX

        // RANGE : [MIN_EXP, MAX_EXP]

        // The minimum exponent value, beneath which underflow to zero occurs.
        // Number type: -324  (5e-324)
        MIN_EXP = -1e7,                          // -1 to -MAX

        // The maximum exponent value, above which overflow to Infinity occurs.
        // Number type:  308  (1.7976931348623157e+308)
        // For MAX_EXP > 1e7, e.g. new BigNumber('1e100000000').plus(1) may be slow.
        MAX_EXP = 1e7,                           // 1 to MAX

        // Whether to use cryptographically-secure random number generation, if available.
        CRYPTO = false,                          // true or false

        // The modulo mode used when calculating the modulus: a mod n.
        // The quotient (q = a / n) is calculated according to the corresponding rounding mode.
        // The remainder (r) is calculated as: r = a - n * q.
        //
        // UP        0 The remainder is positive if the dividend is negative, else is negative.
        // DOWN      1 The remainder has the same sign as the dividend.
        //             This modulo mode is commonly known as 'truncated division' and is
        //             equivalent to (a % n) in JavaScript.
        // FLOOR     3 The remainder has the same sign as the divisor (Python %).
        // HALF_EVEN 6 This modulo mode implements the IEEE 754 remainder function.
        // EUCLID    9 Euclidian division. q = sign(n) * floor(a / abs(n)).
        //             The remainder is always positive.
        //
        // The truncated division, floored division, Euclidian division and IEEE 754 remainder
        // modes are commonly used for the modulus operation.
        // Although the other rounding modes can also be used, they may not give useful results.
        MODULO_MODE = 1,                         // 0 to 9

        // The maximum number of significant digits of the result of the exponentiatedBy operation.
        // If POW_PRECISION is 0, there will be unlimited significant digits.
        POW_PRECISION = 0,                    // 0 to MAX

        // The format specification used by the BigNumber.prototype.toFormat method.
        FORMAT = {
            decimalSeparator: '.',
            groupSeparator: ',',
            groupSize: 3,
            secondaryGroupSize: 0,
            fractionGroupSeparator: '\xA0',      // non-breaking space
            fractionGroupSize: 0
        },

        // The alphabet used for base conversion.
        // It must be at least 2 characters long, with no '.' or repeated character.
        // '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_'
        ALPHABET = '0123456789abcdefghijklmnopqrstuvwxyz';


    //------------------------------------------------------------------------------------------


    // CONSTRUCTOR


    /*
     * The BigNumber constructor and exported function.
     * Create and return a new instance of a BigNumber object.
     *
     * n {number|string|BigNumber} A numeric value.
     * [b] {number} The base of n. Integer, 2 to ALPHABET.length inclusive.
     */
    function BigNumber( n, b ) {
        var alphabet, c, e, i, isNum, len, str,
            x = this;

        // Enable constructor usage without new.
        if ( !( x instanceof BigNumber ) ) {

            // Don't throw on constructor call without new (#81).
            // '[BigNumber Error] Constructor call without new: {n}'
            //throw Error( bignumberError + ' Constructor call without new: ' + n );
            return new BigNumber( n, b );
        }

        if ( b == null ) {

            // Duplicate.
            if ( n instanceof BigNumber ) {
                x.s = n.s;
                x.e = n.e;
                x.c = ( n = n.c ) ? n.slice() : n;
                return;
            }

            isNum = typeof n == 'number';

            if ( isNum && n * 0 == 0 ) {

                // Use `1 / n` to handle minus zero also.
                x.s = 1 / n < 0 ? ( n = -n, -1 ) : 1;

                // Faster path for integers.
                if ( n === ~~n ) {
                    for ( e = 0, i = n; i >= 10; i /= 10, e++ );
                    x.e = e;
                    x.c = [n];
                    return;
                }

                str = n + '';
            } else {
                if ( !isNumeric.test( str = n + '' ) ) return parseNumeric( x, str, isNum );
                x.s = str.charCodeAt(0) == 45 ? ( str = str.slice(1), -1 ) : 1;
            }

        } else {

            // '[BigNumber Error] Base {not a primitive number|not an integer|out of range}: {b}'
            intCheck( b, 2, ALPHABET.length, 'Base' );
            str = n + '';

            // Allow exponential notation to be used with base 10 argument, while
            // also rounding to DECIMAL_PLACES as with other bases.
            if ( b == 10 ) {
                x = new BigNumber( n instanceof BigNumber ? n : str );
                return round( x, DECIMAL_PLACES + x.e + 1, ROUNDING_MODE );
            }

            isNum = typeof n == 'number';

            if (isNum) {

                // Avoid potential interpretation of Infinity and NaN as base 44+ values.
                if ( n * 0 != 0 ) return parseNumeric( x, str, isNum, b );

                x.s = 1 / n < 0 ? ( str = str.slice(1), -1 ) : 1;

                // '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
                if ( str.replace( /^0\.0*|\./, '' ).length > 15 ) {
                    throw Error
                      ( tooManyDigits + n );
                }

                // Prevent later check for length on converted number.
                isNum = false;
            } else {
                x.s = str.charCodeAt(0) === 45 ? ( str = str.slice(1), -1 ) : 1;

                // Allow e.g. hexadecimal 'FF' as well as 'ff'.
                if ( b > 10 && b < 37 ) str = str.toLowerCase();
            }

            alphabet = ALPHABET.slice( 0, b );
            e = i = 0;

            // Check that str is a valid base b number.
            // Don't use RegExp so alphabet can contain special characters.
            for ( len = str.length; i < len; i++ ) {
                if ( alphabet.indexOf( c = str.charAt(i) ) < 0 ) {
                    if ( c == '.' ) {

                        // If '.' is not the first character and it has not be found before.
                        if ( i > e ) {
                            e = len;
                            continue;
                        }
                    }

                    return parseNumeric( x, n + '', isNum, b );
                }
            }

            str = convertBase( str, b, 10, x.s );
        }

        // Decimal point?
        if ( ( e = str.indexOf('.') ) > -1 ) str = str.replace( '.', '' );

        // Exponential form?
        if ( ( i = str.search( /e/i ) ) > 0 ) {

            // Determine exponent.
            if ( e < 0 ) e = i;
            e += +str.slice( i + 1 );
            str = str.substring( 0, i );
        } else if ( e < 0 ) {

            // Integer.
            e = str.length;
        }

        // Determine leading zeros.
        for ( i = 0; str.charCodeAt(i) === 48; i++ );

        // Determine trailing zeros.
        for ( len = str.length; str.charCodeAt(--len) === 48; );
        str = str.slice( i, len + 1 );

        if (str) {
            len = str.length;

            // '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
            if ( isNum && len > 15 && ( n > MAX_SAFE_INTEGER || n !== mathfloor(n) ) ) {
                throw Error
                  ( tooManyDigits + ( x.s * n ) );
            }

            e = e - i - 1;

             // Overflow?
            if ( e > MAX_EXP ) {

                // Infinity.
                x.c = x.e = null;

            // Underflow?
            } else if ( e < MIN_EXP ) {

                // Zero.
                x.c = [ x.e = 0 ];
            } else {
                x.e = e;
                x.c = [];

                // Transform base

                // e is the base 10 exponent.
                // i is where to slice str to get the first element of the coefficient array.
                i = ( e + 1 ) % LOG_BASE;
                if ( e < 0 ) i += LOG_BASE;

                if ( i < len ) {
                    if (i) x.c.push( +str.slice( 0, i ) );

                    for ( len -= LOG_BASE; i < len; ) {
                        x.c.push( +str.slice( i, i += LOG_BASE ) );
                    }

                    str = str.slice(i);
                    i = LOG_BASE - str.length;
                } else {
                    i -= len;
                }

                for ( ; i--; str += '0' );
                x.c.push( +str );
            }
        } else {

            // Zero.
            x.c = [ x.e = 0 ];
        }
    }


    // CONSTRUCTOR PROPERTIES


    BigNumber.clone = clone;

    BigNumber.ROUND_UP = 0;
    BigNumber.ROUND_DOWN = 1;
    BigNumber.ROUND_CEIL = 2;
    BigNumber.ROUND_FLOOR = 3;
    BigNumber.ROUND_HALF_UP = 4;
    BigNumber.ROUND_HALF_DOWN = 5;
    BigNumber.ROUND_HALF_EVEN = 6;
    BigNumber.ROUND_HALF_CEIL = 7;
    BigNumber.ROUND_HALF_FLOOR = 8;
    BigNumber.EUCLID = 9;


    /*
     * Configure infrequently-changing library-wide settings.
     *
     * Accept an object with the following optional properties (if the value of a property is
     * a number, it must be an integer within the inclusive range stated):
     *
     *   DECIMAL_PLACES   {number}           0 to MAX
     *   ROUNDING_MODE    {number}           0 to 8
     *   EXPONENTIAL_AT   {number|number[]}  -MAX to MAX  or  [-MAX to 0, 0 to MAX]
     *   RANGE            {number|number[]}  -MAX to MAX (not zero)  or  [-MAX to -1, 1 to MAX]
     *   CRYPTO           {boolean}          true or false
     *   MODULO_MODE      {number}           0 to 9
     *   POW_PRECISION       {number}           0 to MAX
     *   ALPHABET         {string}           A string of two or more unique characters, and not
     *                                       containing '.'. The empty string, null or undefined
     *                                       resets the alphabet to its default value.
     *   FORMAT           {object}           An object with some of the following properties:
     *      decimalSeparator       {string}
     *      groupSeparator         {string}
     *      groupSize              {number}
     *      secondaryGroupSize     {number}
     *      fractionGroupSeparator {string}
     *      fractionGroupSize      {number}
     *
     * (The values assigned to the above FORMAT object properties are not checked for validity.)
     *
     * E.g.
     * BigNumber.config({ DECIMAL_PLACES : 20, ROUNDING_MODE : 4 })
     *
     * Ignore properties/parameters set to null or undefined, except for ALPHABET.
     *
     * Return an object with the properties current values.
     */
    BigNumber.config = BigNumber.set = function (obj) {
        var p, v;

        if ( obj != null ) {

            if ( typeof obj == 'object' ) {

                // DECIMAL_PLACES {number} Integer, 0 to MAX inclusive.
                // '[BigNumber Error] DECIMAL_PLACES {not a primitive number|not an integer|out of range}: {v}'
                if ( obj.hasOwnProperty( p = 'DECIMAL_PLACES' ) ) {
                    v = obj[p];
                    intCheck( v, 0, MAX, p );
                    DECIMAL_PLACES = v;
                }

                // ROUNDING_MODE {number} Integer, 0 to 8 inclusive.
                // '[BigNumber Error] ROUNDING_MODE {not a primitive number|not an integer|out of range}: {v}'
                if ( obj.hasOwnProperty( p = 'ROUNDING_MODE' ) ) {
                    v = obj[p];
                    intCheck( v, 0, 8, p );
                    ROUNDING_MODE = v;
                }

                // EXPONENTIAL_AT {number|number[]}
                // Integer, -MAX to MAX inclusive or
                // [integer -MAX to 0 inclusive, 0 to MAX inclusive].
                // '[BigNumber Error] EXPONENTIAL_AT {not a primitive number|not an integer|out of range}: {v}'
                if ( obj.hasOwnProperty( p = 'EXPONENTIAL_AT' ) ) {
                    v = obj[p];
                    if ( isArray(v) ) {
                        intCheck( v[0], -MAX, 0, p );
                        intCheck( v[1], 0, MAX, p );
                        TO_EXP_NEG = v[0];
                        TO_EXP_POS = v[1];
                    } else {
                        intCheck( v, -MAX, MAX, p );
                        TO_EXP_NEG = -( TO_EXP_POS = v < 0 ? -v : v );
                    }
                }

                // RANGE {number|number[]} Non-zero integer, -MAX to MAX inclusive or
                // [integer -MAX to -1 inclusive, integer 1 to MAX inclusive].
                // '[BigNumber Error] RANGE {not a primitive number|not an integer|out of range|cannot be zero}: {v}'
                if ( obj.hasOwnProperty( p = 'RANGE' ) ) {
                    v = obj[p];
                    if ( isArray(v) ) {
                        intCheck( v[0], -MAX, -1, p );
                        intCheck( v[1], 1, MAX, p );
                        MIN_EXP = v[0];
                        MAX_EXP = v[1];
                    } else {
                        intCheck( v, -MAX, MAX, p );
                        if (v) {
                            MIN_EXP = -( MAX_EXP = v < 0 ? -v : v );
                        } else {
                            throw Error
                              ( bignumberError + p + ' cannot be zero: ' + v );
                        }
                    }
                }

                // CRYPTO {boolean} true or false.
                // '[BigNumber Error] CRYPTO not true or false: {v}'
                // '[BigNumber Error] crypto unavailable'
                if ( obj.hasOwnProperty( p = 'CRYPTO' ) ) {
                    v = obj[p];
                    if ( v === !!v ) {
                        if (v) {
                            if ( typeof crypto != 'undefined' && crypto &&
                              (crypto.getRandomValues || crypto.randomBytes) ) {
                                CRYPTO = v;
                            } else {
                                CRYPTO = !v;
                                throw Error
                                  ( bignumberError + 'crypto unavailable' );
                            }
                        } else {
                            CRYPTO = v;
                        }
                    } else {
                        throw Error
                          ( bignumberError + p + ' not true or false: ' + v );
                    }
                }

                // MODULO_MODE {number} Integer, 0 to 9 inclusive.
                // '[BigNumber Error] MODULO_MODE {not a primitive number|not an integer|out of range}: {v}'
                if ( obj.hasOwnProperty( p = 'MODULO_MODE' ) ) {
                    v = obj[p];
                    intCheck( v, 0, 9, p );
                    MODULO_MODE = v;
                }

                // POW_PRECISION {number} Integer, 0 to MAX inclusive.
                // '[BigNumber Error] POW_PRECISION {not a primitive number|not an integer|out of range}: {v}'
                if ( obj.hasOwnProperty( p = 'POW_PRECISION' ) ) {
                    v = obj[p];
                    intCheck( v, 0, MAX, p );
                    POW_PRECISION = v;
                }

                // FORMAT {object}
                // '[BigNumber Error] FORMAT not an object: {v}'
                if ( obj.hasOwnProperty( p = 'FORMAT' ) ) {
                    v = obj[p];
                    if ( typeof v == 'object' ) FORMAT = v;
                    else throw Error
                      ( bignumberError + p + ' not an object: ' + v );
                }

                // ALPHABET {string}
                // '[BigNumber Error] ALPHABET invalid: {v}'
                if ( obj.hasOwnProperty( p = 'ALPHABET' ) ) {
                    v = obj[p];

                    // Disallow if only one character, or contains '.' or a repeated character.
                    if ( typeof v == 'string' && !/^.$|\.|(.).*\1/.test(v) ) {
                        ALPHABET = v;
                    } else {
                        throw Error
                          ( bignumberError + p + ' invalid: ' + v );
                    }
                }

            } else {

                // '[BigNumber Error] Object expected: {v}'
                throw Error
                  ( bignumberError + 'Object expected: ' + obj );
            }
        }

        return {
            DECIMAL_PLACES: DECIMAL_PLACES,
            ROUNDING_MODE: ROUNDING_MODE,
            EXPONENTIAL_AT: [ TO_EXP_NEG, TO_EXP_POS ],
            RANGE: [ MIN_EXP, MAX_EXP ],
            CRYPTO: CRYPTO,
            MODULO_MODE: MODULO_MODE,
            POW_PRECISION: POW_PRECISION,
            FORMAT: FORMAT,
            ALPHABET: ALPHABET
        };
    };


    /*
     * Return true if v is a BigNumber instance, otherwise return false.
     *
     * v {any}
     */
    BigNumber.isBigNumber = function (v) {
        return v instanceof BigNumber || v && v._isBigNumber === true || false;
    };


    /*
     * Return a new BigNumber whose value is the maximum of the arguments.
     *
     * arguments {number|string|BigNumber}
     */
    BigNumber.maximum = BigNumber.max = function () {
        return maxOrMin( arguments, P.lt );
    };


    /*
     * Return a new BigNumber whose value is the minimum of the arguments.
     *
     * arguments {number|string|BigNumber}
     */
    BigNumber.minimum = BigNumber.min = function () {
        return maxOrMin( arguments, P.gt );
    };


    /*
     * Return a new BigNumber with a random value equal to or greater than 0 and less than 1,
     * and with dp, or DECIMAL_PLACES if dp is omitted, decimal places (or less if trailing
     * zeros are produced).
     *
     * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
     *
     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp}'
     * '[BigNumber Error] crypto unavailable'
     */
    BigNumber.random = (function () {
        var pow2_53 = 0x20000000000000;

        // Return a 53 bit integer n, where 0 <= n < 9007199254740992.
        // Check if Math.random() produces more than 32 bits of randomness.
        // If it does, assume at least 53 bits are produced, otherwise assume at least 30 bits.
        // 0x40000000 is 2^30, 0x800000 is 2^23, 0x1fffff is 2^21 - 1.
        var random53bitInt = (Math.random() * pow2_53) & 0x1fffff
          ? function () { return mathfloor( Math.random() * pow2_53 ); }
          : function () { return ((Math.random() * 0x40000000 | 0) * 0x800000) +
              (Math.random() * 0x800000 | 0); };

        return function (dp) {
            var a, b, e, k, v,
                i = 0,
                c = [],
                rand = new BigNumber(ONE);

            if ( dp == null ) dp = DECIMAL_PLACES;
            else intCheck( dp, 0, MAX );

            k = mathceil( dp / LOG_BASE );

            if (CRYPTO) {

                // Browsers supporting crypto.getRandomValues.
                if (crypto.getRandomValues) {

                    a = crypto.getRandomValues( new Uint32Array( k *= 2 ) );

                    for ( ; i < k; ) {

                        // 53 bits:
                        // ((Math.pow(2, 32) - 1) * Math.pow(2, 21)).toString(2)
                        // 11111 11111111 11111111 11111111 11100000 00000000 00000000
                        // ((Math.pow(2, 32) - 1) >>> 11).toString(2)
                        //                                     11111 11111111 11111111
                        // 0x20000 is 2^21.
                        v = a[i] * 0x20000 + (a[i + 1] >>> 11);

                        // Rejection sampling:
                        // 0 <= v < 9007199254740992
                        // Probability that v >= 9e15, is
                        // 7199254740992 / 9007199254740992 ~= 0.0008, i.e. 1 in 1251
                        if ( v >= 9e15 ) {
                            b = crypto.getRandomValues( new Uint32Array(2) );
                            a[i] = b[0];
                            a[i + 1] = b[1];
                        } else {

                            // 0 <= v <= 8999999999999999
                            // 0 <= (v % 1e14) <= 99999999999999
                            c.push( v % 1e14 );
                            i += 2;
                        }
                    }
                    i = k / 2;

                // Node.js supporting crypto.randomBytes.
                } else if (crypto.randomBytes) {

                    // buffer
                    a = crypto.randomBytes( k *= 7 );

                    for ( ; i < k; ) {

                        // 0x1000000000000 is 2^48, 0x10000000000 is 2^40
                        // 0x100000000 is 2^32, 0x1000000 is 2^24
                        // 11111 11111111 11111111 11111111 11111111 11111111 11111111
                        // 0 <= v < 9007199254740992
                        v = ( ( a[i] & 31 ) * 0x1000000000000 ) + ( a[i + 1] * 0x10000000000 ) +
                              ( a[i + 2] * 0x100000000 ) + ( a[i + 3] * 0x1000000 ) +
                              ( a[i + 4] << 16 ) + ( a[i + 5] << 8 ) + a[i + 6];

                        if ( v >= 9e15 ) {
                            crypto.randomBytes(7).copy( a, i );
                        } else {

                            // 0 <= (v % 1e14) <= 99999999999999
                            c.push( v % 1e14 );
                            i += 7;
                        }
                    }
                    i = k / 7;
                } else {
                    CRYPTO = false;
                    throw Error
                      ( bignumberError + 'crypto unavailable' );
                }
            }

            // Use Math.random.
            if (!CRYPTO) {

                for ( ; i < k; ) {
                    v = random53bitInt();
                    if ( v < 9e15 ) c[i++] = v % 1e14;
                }
            }

            k = c[--i];
            dp %= LOG_BASE;

            // Convert trailing digits to zeros according to dp.
            if ( k && dp ) {
                v = POWS_TEN[LOG_BASE - dp];
                c[i] = mathfloor( k / v ) * v;
            }

            // Remove trailing elements which are zero.
            for ( ; c[i] === 0; c.pop(), i-- );

            // Zero?
            if ( i < 0 ) {
                c = [ e = 0 ];
            } else {

                // Remove leading elements which are zero and adjust exponent accordingly.
                for ( e = -1 ; c[0] === 0; c.splice(0, 1), e -= LOG_BASE);

                // Count the digits of the first element of c to determine leading zeros, and...
                for ( i = 1, v = c[0]; v >= 10; v /= 10, i++);

                // adjust the exponent accordingly.
                if ( i < LOG_BASE ) e -= LOG_BASE - i;
            }

            rand.e = e;
            rand.c = c;
            return rand;
        };
    })();


    // PRIVATE FUNCTIONS


    // Called by BigNumber and BigNumber.prototype.toString.
    convertBase = ( function () {
        var decimal = '0123456789';

        /*
         * Convert string of baseIn to an array of numbers of baseOut.
         * Eg. toBaseOut('255', 10, 16) returns [15, 15].
         * Eg. toBaseOut('ff', 16, 10) returns [2, 5, 5].
         */
        function toBaseOut( str, baseIn, baseOut, alphabet ) {
            var j,
                arr = [0],
                arrL,
                i = 0,
                len = str.length;

            for ( ; i < len; ) {
                for ( arrL = arr.length; arrL--; arr[arrL] *= baseIn );

                arr[0] += alphabet.indexOf( str.charAt( i++ ) );

                for ( j = 0; j < arr.length; j++ ) {

                    if ( arr[j] > baseOut - 1 ) {
                        if ( arr[j + 1] == null ) arr[j + 1] = 0;
                        arr[j + 1] += arr[j] / baseOut | 0;
                        arr[j] %= baseOut;
                    }
                }
            }

            return arr.reverse();
        }

        // Convert a numeric string of baseIn to a numeric string of baseOut.
        // If the caller is toString, we are converting from base 10 to baseOut.
        // If the caller is BigNumber, we are converting from baseIn to base 10.
        return function ( str, baseIn, baseOut, sign, callerIsToString ) {
            var alphabet, d, e, k, r, x, xc, y,
                i = str.indexOf( '.' ),
                dp = DECIMAL_PLACES,
                rm = ROUNDING_MODE;

            // Non-integer.
            if ( i >= 0 ) {
                k = POW_PRECISION;

                // Unlimited precision.
                POW_PRECISION = 0;
                str = str.replace( '.', '' );
                y = new BigNumber(baseIn);
                x = y.pow( str.length - i );
                POW_PRECISION = k;

                // Convert str as if an integer, then restore the fraction part by dividing the
                // result by its base raised to a power.

                y.c = toBaseOut( toFixedPoint( coeffToString( x.c ), x.e, '0' ),
                  10, baseOut, decimal );
                y.e = y.c.length;
            }

            // Convert the number as integer.

            xc = toBaseOut( str, baseIn, baseOut, callerIsToString
              ? ( alphabet = ALPHABET, decimal )
              : ( alphabet = decimal, ALPHABET ) );


            // xc now represents str as an integer and converted to baseOut. e is the exponent.
            e = k = xc.length;

            // Remove trailing zeros.
            for ( ; xc[--k] == 0; xc.pop() );

            // Zero?
            if ( !xc[0] ) return alphabet.charAt(0);

            // Does str represent an integer? If so, no need for the division.
            if ( i < 0 ) {
                --e;
            } else {
                x.c = xc;
                x.e = e;

                // The sign is needed for correct rounding.
                x.s = sign;
                x = div( x, y, dp, rm, baseOut );
                xc = x.c;
                r = x.r;
                e = x.e;
            }

            // xc now represents str converted to baseOut.

            // THe index of the rounding digit.
            d = e + dp + 1;

            // The rounding digit: the digit to the right of the digit that may be rounded up.
            i = xc[d];

            // Look at the rounding digits and mode to determine whether to round up.

            k = baseOut / 2;
            r = r || d < 0 || xc[d + 1] != null;

            r = rm < 4 ? ( i != null || r ) && ( rm == 0 || rm == ( x.s < 0 ? 3 : 2 ) )
                       : i > k || i == k &&( rm == 4 || r || rm == 6 && xc[d - 1] & 1 ||
                         rm == ( x.s < 0 ? 8 : 7 ) );

            // If the index of the rounding digit is not greater than zero, or xc represents
            // zero, then the result of the base conversion is zero or, if rounding up, a value
            // such as 0.00001.
            if ( d < 1 || !xc[0] ) {

                // 1^-dp or 0
                str = r ? toFixedPoint( alphabet.charAt(1), -dp, alphabet.charAt(0) )
                        : alphabet.charAt(0);
            } else {

                // Truncate xc to the required number of decimal places.
                xc.length = d;

                // Round up?
                if (r) {

                    // Rounding up may mean the previous digit has to be rounded up and so on.
                    for ( --baseOut; ++xc[--d] > baseOut; ) {
                        xc[d] = 0;

                        if ( !d ) {
                            ++e;
                            xc = [1].concat(xc);
                        }
                    }
                }

                // Determine trailing zeros.
                for ( k = xc.length; !xc[--k]; );

                // E.g. [4, 11, 15] becomes 4bf.
                for ( i = 0, str = ''; i <= k; str += alphabet.charAt( xc[i++] ) );

                // Add leading zeros, decimal point and trailing zeros as required.
                str = toFixedPoint( str, e, alphabet.charAt(0) );
            }

            // The caller will add the sign.
            return str;
        };
    })();


    // Perform division in the specified base. Called by div and convertBase.
    div = (function () {

        // Assume non-zero x and k.
        function multiply( x, k, base ) {
            var m, temp, xlo, xhi,
                carry = 0,
                i = x.length,
                klo = k % SQRT_BASE,
                khi = k / SQRT_BASE | 0;

            for ( x = x.slice(); i--; ) {
                xlo = x[i] % SQRT_BASE;
                xhi = x[i] / SQRT_BASE | 0;
                m = khi * xlo + xhi * klo;
                temp = klo * xlo + ( ( m % SQRT_BASE ) * SQRT_BASE ) + carry;
                carry = ( temp / base | 0 ) + ( m / SQRT_BASE | 0 ) + khi * xhi;
                x[i] = temp % base;
            }

            if (carry) x = [carry].concat(x);

            return x;
        }

        function compare( a, b, aL, bL ) {
            var i, cmp;

            if ( aL != bL ) {
                cmp = aL > bL ? 1 : -1;
            } else {

                for ( i = cmp = 0; i < aL; i++ ) {

                    if ( a[i] != b[i] ) {
                        cmp = a[i] > b[i] ? 1 : -1;
                        break;
                    }
                }
            }
            return cmp;
        }

        function subtract( a, b, aL, base ) {
            var i = 0;

            // Subtract b from a.
            for ( ; aL--; ) {
                a[aL] -= i;
                i = a[aL] < b[aL] ? 1 : 0;
                a[aL] = i * base + a[aL] - b[aL];
            }

            // Remove leading zeros.
            for ( ; !a[0] && a.length > 1; a.splice(0, 1) );
        }

        // x: dividend, y: divisor.
        return function ( x, y, dp, rm, base ) {
            var cmp, e, i, more, n, prod, prodL, q, qc, rem, remL, rem0, xi, xL, yc0,
                yL, yz,
                s = x.s == y.s ? 1 : -1,
                xc = x.c,
                yc = y.c;

            // Either NaN, Infinity or 0?
            if ( !xc || !xc[0] || !yc || !yc[0] ) {

                return new BigNumber(

                  // Return NaN if either NaN, or both Infinity or 0.
                  !x.s || !y.s || ( xc ? yc && xc[0] == yc[0] : !yc ) ? NaN :

                    // Return ±0 if x is ±0 or y is ±Infinity, or return ±Infinity as y is ±0.
                    xc && xc[0] == 0 || !yc ? s * 0 : s / 0
                );
            }

            q = new BigNumber(s);
            qc = q.c = [];
            e = x.e - y.e;
            s = dp + e + 1;

            if ( !base ) {
                base = BASE;
                e = bitFloor( x.e / LOG_BASE ) - bitFloor( y.e / LOG_BASE );
                s = s / LOG_BASE | 0;
            }

            // Result exponent may be one less then the current value of e.
            // The coefficients of the BigNumbers from convertBase may have trailing zeros.
            for ( i = 0; yc[i] == ( xc[i] || 0 ); i++ );

            if ( yc[i] > ( xc[i] || 0 ) ) e--;

            if ( s < 0 ) {
                qc.push(1);
                more = true;
            } else {
                xL = xc.length;
                yL = yc.length;
                i = 0;
                s += 2;

                // Normalise xc and yc so highest order digit of yc is >= base / 2.

                n = mathfloor( base / ( yc[0] + 1 ) );

                // Not necessary, but to handle odd bases where yc[0] == ( base / 2 ) - 1.
                // if ( n > 1 || n++ == 1 && yc[0] < base / 2 ) {
                if ( n > 1 ) {
                    yc = multiply( yc, n, base );
                    xc = multiply( xc, n, base );
                    yL = yc.length;
                    xL = xc.length;
                }

                xi = yL;
                rem = xc.slice( 0, yL );
                remL = rem.length;

                // Add zeros to make remainder as long as divisor.
                for ( ; remL < yL; rem[remL++] = 0 );
                yz = yc.slice();
                yz = [0].concat(yz);
                yc0 = yc[0];
                if ( yc[1] >= base / 2 ) yc0++;
                // Not necessary, but to prevent trial digit n > base, when using base 3.
                // else if ( base == 3 && yc0 == 1 ) yc0 = 1 + 1e-15;

                do {
                    n = 0;

                    // Compare divisor and remainder.
                    cmp = compare( yc, rem, yL, remL );

                    // If divisor < remainder.
                    if ( cmp < 0 ) {

                        // Calculate trial digit, n.

                        rem0 = rem[0];
                        if ( yL != remL ) rem0 = rem0 * base + ( rem[1] || 0 );

                        // n is how many times the divisor goes into the current remainder.
                        n = mathfloor( rem0 / yc0 );

                        //  Algorithm:
                        //  1. product = divisor * trial digit (n)
                        //  2. if product > remainder: product -= divisor, n--
                        //  3. remainder -= product
                        //  4. if product was < remainder at 2:
                        //    5. compare new remainder and divisor
                        //    6. If remainder > divisor: remainder -= divisor, n++

                        if ( n > 1 ) {

                            // n may be > base only when base is 3.
                            if (n >= base) n = base - 1;

                            // product = divisor * trial digit.
                            prod = multiply( yc, n, base );
                            prodL = prod.length;
                            remL = rem.length;

                            // Compare product and remainder.
                            // If product > remainder.
                            // Trial digit n too high.
                            // n is 1 too high about 5% of the time, and is not known to have
                            // ever been more than 1 too high.
                            while ( compare( prod, rem, prodL, remL ) == 1 ) {
                                n--;

                                // Subtract divisor from product.
                                subtract( prod, yL < prodL ? yz : yc, prodL, base );
                                prodL = prod.length;
                                cmp = 1;
                            }
                        } else {

                            // n is 0 or 1, cmp is -1.
                            // If n is 0, there is no need to compare yc and rem again below,
                            // so change cmp to 1 to avoid it.
                            // If n is 1, leave cmp as -1, so yc and rem are compared again.
                            if ( n == 0 ) {

                                // divisor < remainder, so n must be at least 1.
                                cmp = n = 1;
                            }

                            // product = divisor
                            prod = yc.slice();
                            prodL = prod.length;
                        }

                        if ( prodL < remL ) prod = [0].concat(prod);

                        // Subtract product from remainder.
                        subtract( rem, prod, remL, base );
                        remL = rem.length;

                         // If product was < remainder.
                        if ( cmp == -1 ) {

                            // Compare divisor and new remainder.
                            // If divisor < new remainder, subtract divisor from remainder.
                            // Trial digit n too low.
                            // n is 1 too low about 5% of the time, and very rarely 2 too low.
                            while ( compare( yc, rem, yL, remL ) < 1 ) {
                                n++;

                                // Subtract divisor from remainder.
                                subtract( rem, yL < remL ? yz : yc, remL, base );
                                remL = rem.length;
                            }
                        }
                    } else if ( cmp === 0 ) {
                        n++;
                        rem = [0];
                    } // else cmp === 1 and n will be 0

                    // Add the next digit, n, to the result array.
                    qc[i++] = n;

                    // Update the remainder.
                    if ( rem[0] ) {
                        rem[remL++] = xc[xi] || 0;
                    } else {
                        rem = [ xc[xi] ];
                        remL = 1;
                    }
                } while ( ( xi++ < xL || rem[0] != null ) && s-- );

                more = rem[0] != null;

                // Leading zero?
                if ( !qc[0] ) qc.splice(0, 1);
            }

            if ( base == BASE ) {

                // To calculate q.e, first get the number of digits of qc[0].
                for ( i = 1, s = qc[0]; s >= 10; s /= 10, i++ );

                round( q, dp + ( q.e = i + e * LOG_BASE - 1 ) + 1, rm, more );

            // Caller is convertBase.
            } else {
                q.e = e;
                q.r = +more;
            }

            return q;
        };
    })();


    /*
     * Return a string representing the value of BigNumber n in fixed-point or exponential
     * notation rounded to the specified decimal places or significant digits.
     *
     * n: a BigNumber.
     * i: the index of the last digit required (i.e. the digit that may be rounded up).
     * rm: the rounding mode.
     * id: 1 (toExponential) or 2 (toPrecision).
     */
    function format( n, i, rm, id ) {
        var c0, e, ne, len, str;

        if ( rm == null ) rm = ROUNDING_MODE;
        else intCheck( rm, 0, 8 );

        if ( !n.c ) return n.toString();

        c0 = n.c[0];
        ne = n.e;

        if ( i == null ) {
            str = coeffToString( n.c );
            str = id == 1 || id == 2 && ne <= TO_EXP_NEG
              ? toExponential( str, ne )
              : toFixedPoint( str, ne, '0' );
        } else {
            n = round( new BigNumber(n), i, rm );

            // n.e may have changed if the value was rounded up.
            e = n.e;

            str = coeffToString( n.c );
            len = str.length;

            // toPrecision returns exponential notation if the number of significant digits
            // specified is less than the number of digits necessary to represent the integer
            // part of the value in fixed-point notation.

            // Exponential notation.
            if ( id == 1 || id == 2 && ( i <= e || e <= TO_EXP_NEG ) ) {

                // Append zeros?
                for ( ; len < i; str += '0', len++ );
                str = toExponential( str, e );

            // Fixed-point notation.
            } else {
                i -= ne;
                str = toFixedPoint( str, e, '0' );

                // Append zeros?
                if ( e + 1 > len ) {
                    if ( --i > 0 ) for ( str += '.'; i--; str += '0' );
                } else {
                    i += e - len;
                    if ( i > 0 ) {
                        if ( e + 1 == len ) str += '.';
                        for ( ; i--; str += '0' );
                    }
                }
            }
        }

        return n.s < 0 && c0 ? '-' + str : str;
    }


    // Handle BigNumber.max and BigNumber.min.
    function maxOrMin( args, method ) {
        var m, n,
            i = 0;

        if ( isArray( args[0] ) ) args = args[0];
        m = new BigNumber( args[0] );

        for ( ; ++i < args.length; ) {
            n = new BigNumber( args[i] );

            // If any number is NaN, return NaN.
            if ( !n.s ) {
                m = n;
                break;
            } else if ( method.call( m, n ) ) {
                m = n;
            }
        }

        return m;
    }


    /*
     * Strip trailing zeros, calculate base 10 exponent and check against MIN_EXP and MAX_EXP.
     * Called by minus, plus and times.
     */
    function normalise( n, c, e ) {
        var i = 1,
            j = c.length;

         // Remove trailing zeros.
        for ( ; !c[--j]; c.pop() );

        // Calculate the base 10 exponent. First get the number of digits of c[0].
        for ( j = c[0]; j >= 10; j /= 10, i++ );

        // Overflow?
        if ( ( e = i + e * LOG_BASE - 1 ) > MAX_EXP ) {

            // Infinity.
            n.c = n.e = null;

        // Underflow?
        } else if ( e < MIN_EXP ) {

            // Zero.
            n.c = [ n.e = 0 ];
        } else {
            n.e = e;
            n.c = c;
        }

        return n;
    }


    // Handle values that fail the validity test in BigNumber.
    parseNumeric = (function () {
        var basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i,
            dotAfter = /^([^.]+)\.$/,
            dotBefore = /^\.([^.]+)$/,
            isInfinityOrNaN = /^-?(Infinity|NaN)$/,
            whitespaceOrPlus = /^\s*\+(?=[\w.])|^\s+|\s+$/g;

        return function ( x, str, isNum, b ) {
            var base,
                s = isNum ? str : str.replace( whitespaceOrPlus, '' );

            // No exception on ±Infinity or NaN.
            if ( isInfinityOrNaN.test(s) ) {
                x.s = isNaN(s) ? null : s < 0 ? -1 : 1;
                x.c = x.e = null;
            } else {
                if ( !isNum ) {

                    // basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i
                    s = s.replace( basePrefix, function ( m, p1, p2 ) {
                        base = ( p2 = p2.toLowerCase() ) == 'x' ? 16 : p2 == 'b' ? 2 : 8;
                        return !b || b == base ? p1 : m;
                    });

                    if (b) {
                        base = b;

                        // E.g. '1.' to '1', '.1' to '0.1'
                        s = s.replace( dotAfter, '$1' ).replace( dotBefore, '0.$1' );
                    }

                    if ( str != s ) return new BigNumber( s, base );
                }

                // '[BigNumber Error] Not a number: {n}'
                // '[BigNumber Error] Not a base {b} number: {n}'
                throw Error
                  ( bignumberError + 'Not a' + ( b ? ' base ' + b : '' ) + ' number: ' + str );
            }
        }
    })();


    /*
     * Round x to sd significant digits using rounding mode rm. Check for over/under-flow.
     * If r is truthy, it is known that there are more digits after the rounding digit.
     */
    function round( x, sd, rm, r ) {
        var d, i, j, k, n, ni, rd,
            xc = x.c,
            pows10 = POWS_TEN;

        // if x is not Infinity or NaN...
        if (xc) {

            // rd is the rounding digit, i.e. the digit after the digit that may be rounded up.
            // n is a base 1e14 number, the value of the element of array x.c containing rd.
            // ni is the index of n within x.c.
            // d is the number of digits of n.
            // i is the index of rd within n including leading zeros.
            // j is the actual index of rd within n (if < 0, rd is a leading zero).
            out: {

                // Get the number of digits of the first element of xc.
                for ( d = 1, k = xc[0]; k >= 10; k /= 10, d++ );
                i = sd - d;

                // If the rounding digit is in the first element of xc...
                if ( i < 0 ) {
                    i += LOG_BASE;
                    j = sd;
                    n = xc[ ni = 0 ];

                    // Get the rounding digit at index j of n.
                    rd = n / pows10[ d - j - 1 ] % 10 | 0;
                } else {
                    ni = mathceil( ( i + 1 ) / LOG_BASE );

                    if ( ni >= xc.length ) {

                        if (r) {

                            // Needed by sqrt.
                            for ( ; xc.length <= ni; xc.push(0) );
                            n = rd = 0;
                            d = 1;
                            i %= LOG_BASE;
                            j = i - LOG_BASE + 1;
                        } else {
                            break out;
                        }
                    } else {
                        n = k = xc[ni];

                        // Get the number of digits of n.
                        for ( d = 1; k >= 10; k /= 10, d++ );

                        // Get the index of rd within n.
                        i %= LOG_BASE;

                        // Get the index of rd within n, adjusted for leading zeros.
                        // The number of leading zeros of n is given by LOG_BASE - d.
                        j = i - LOG_BASE + d;

                        // Get the rounding digit at index j of n.
                        rd = j < 0 ? 0 : n / pows10[ d - j - 1 ] % 10 | 0;
                    }
                }

                r = r || sd < 0 ||

                // Are there any non-zero digits after the rounding digit?
                // The expression  n % pows10[ d - j - 1 ]  returns all digits of n to the right
                // of the digit at j, e.g. if n is 908714 and j is 2, the expression gives 714.
                  xc[ni + 1] != null || ( j < 0 ? n : n % pows10[ d - j - 1 ] );

                r = rm < 4
                  ? ( rd || r ) && ( rm == 0 || rm == ( x.s < 0 ? 3 : 2 ) )
                  : rd > 5 || rd == 5 && ( rm == 4 || r || rm == 6 &&

                    // Check whether the digit to the left of the rounding digit is odd.
                    ( ( i > 0 ? j > 0 ? n / pows10[ d - j ] : 0 : xc[ni - 1] ) % 10 ) & 1 ||
                      rm == ( x.s < 0 ? 8 : 7 ) );

                if ( sd < 1 || !xc[0] ) {
                    xc.length = 0;

                    if (r) {

                        // Convert sd to decimal places.
                        sd -= x.e + 1;

                        // 1, 0.1, 0.01, 0.001, 0.0001 etc.
                        xc[0] = pows10[ ( LOG_BASE - sd % LOG_BASE ) % LOG_BASE ];
                        x.e = -sd || 0;
                    } else {

                        // Zero.
                        xc[0] = x.e = 0;
                    }

                    return x;
                }

                // Remove excess digits.
                if ( i == 0 ) {
                    xc.length = ni;
                    k = 1;
                    ni--;
                } else {
                    xc.length = ni + 1;
                    k = pows10[ LOG_BASE - i ];

                    // E.g. 56700 becomes 56000 if 7 is the rounding digit.
                    // j > 0 means i > number of leading zeros of n.
                    xc[ni] = j > 0 ? mathfloor( n / pows10[ d - j ] % pows10[j] ) * k : 0;
                }

                // Round up?
                if (r) {

                    for ( ; ; ) {

                        // If the digit to be rounded up is in the first element of xc...
                        if ( ni == 0 ) {

                            // i will be the length of xc[0] before k is added.
                            for ( i = 1, j = xc[0]; j >= 10; j /= 10, i++ );
                            j = xc[0] += k;
                            for ( k = 1; j >= 10; j /= 10, k++ );

                            // if i != k the length has increased.
                            if ( i != k ) {
                                x.e++;
                                if ( xc[0] == BASE ) xc[0] = 1;
                            }

                            break;
                        } else {
                            xc[ni] += k;
                            if ( xc[ni] != BASE ) break;
                            xc[ni--] = 0;
                            k = 1;
                        }
                    }
                }

                // Remove trailing zeros.
                for ( i = xc.length; xc[--i] === 0; xc.pop() );
            }

            // Overflow? Infinity.
            if ( x.e > MAX_EXP ) {
                x.c = x.e = null;

            // Underflow? Zero.
            } else if ( x.e < MIN_EXP ) {
                x.c = [ x.e = 0 ];
            }
        }

        return x;
    }


    // PROTOTYPE/INSTANCE METHODS


    /*
     * Return a new BigNumber whose value is the absolute value of this BigNumber.
     */
    P.absoluteValue = P.abs = function () {
        var x = new BigNumber(this);
        if ( x.s < 0 ) x.s = 1;
        return x;
    };


    /*
     * Return
     *   1 if the value of this BigNumber is greater than the value of BigNumber(y, b),
     *   -1 if the value of this BigNumber is less than the value of BigNumber(y, b),
     *   0 if they have the same value,
     *   or null if the value of either is NaN.
     */
    P.comparedTo = function ( y, b ) {
        return compare( this, new BigNumber( y, b ) );
    };


    /*
     * If dp is undefined or null or true or false, return the number of decimal places of the
     * value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN.
     *
     * Otherwise, if dp is a number, return a new BigNumber whose value is the value of this
     * BigNumber rounded to a maximum of dp decimal places using rounding mode rm, or
     * ROUNDING_MODE if rm is omitted.
     *
     * [dp] {number} Decimal places: integer, 0 to MAX inclusive.
     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
     *
     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
     */
    P.decimalPlaces = P.dp = function ( dp, rm ) {
        var c, n, v,
            x = this;

        if ( dp != null ) {
            intCheck( dp, 0, MAX );
            if ( rm == null ) rm = ROUNDING_MODE;
            else intCheck( rm, 0, 8 );

            return round( new BigNumber(x), dp + x.e + 1, rm );
        }

        if ( !( c = x.c ) ) return null;
        n = ( ( v = c.length - 1 ) - bitFloor( this.e / LOG_BASE ) ) * LOG_BASE;

        // Subtract the number of trailing zeros of the last number.
        if ( v = c[v] ) for ( ; v % 10 == 0; v /= 10, n-- );
        if ( n < 0 ) n = 0;

        return n;
    };


    /*
     *  n / 0 = I
     *  n / N = N
     *  n / I = 0
     *  0 / n = 0
     *  0 / 0 = N
     *  0 / N = N
     *  0 / I = 0
     *  N / n = N
     *  N / 0 = N
     *  N / N = N
     *  N / I = N
     *  I / n = I
     *  I / 0 = I
     *  I / N = N
     *  I / I = N
     *
     * Return a new BigNumber whose value is the value of this BigNumber divided by the value of
     * BigNumber(y, b), rounded according to DECIMAL_PLACES and ROUNDING_MODE.
     */
    P.dividedBy = P.div = function ( y, b ) {
        return div( this, new BigNumber( y, b ), DECIMAL_PLACES, ROUNDING_MODE );
    };


    /*
     * Return a new BigNumber whose value is the integer part of dividing the value of this
     * BigNumber by the value of BigNumber(y, b).
     */
    P.dividedToIntegerBy = P.idiv = function ( y, b ) {
        return div( this, new BigNumber( y, b ), 0, 1 );
    };


    /*
     * Return true if the value of this BigNumber is equal to the value of BigNumber(y, b),
     * otherwise return false.
     */
    P.isEqualTo = P.eq = function ( y, b ) {
        return compare( this, new BigNumber( y, b ) ) === 0;
    };


    /*
     * Return a new BigNumber whose value is the value of this BigNumber rounded to an integer
     * using rounding mode rm, or ROUNDING_MODE if rm is omitted.
     *
     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
     *
     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {rm}'
     */
    P.integerValue = function (rm) {
        var n = new BigNumber(this);
        if ( rm == null ) rm = ROUNDING_MODE;
        else intCheck( rm, 0, 8 );
        return round( n, n.e + 1, rm );
    };


    /*
     * Return true if the value of this BigNumber is greater than the value of BigNumber(y, b),
     * otherwise return false.
     */
    P.isGreaterThan = P.gt = function ( y, b ) {
        return compare( this, new BigNumber( y, b ) ) > 0;
    };


    /*
     * Return true if the value of this BigNumber is greater than or equal to the value of
     * BigNumber(y, b), otherwise return false.
     */
    P.isGreaterThanOrEqualTo = P.gte = function ( y, b ) {
        return ( b = compare( this, new BigNumber( y, b ) ) ) === 1 || b === 0;

    };


    /*
     * Return true if the value of this BigNumber is a finite number, otherwise return false.
     */
    P.isFinite = function () {
        return !!this.c;
    };


    /*
     * Return true if the value of this BigNumber is an integer, otherwise return false.
     */
    P.isInteger = function () {
        return !!this.c && bitFloor( this.e / LOG_BASE ) > this.c.length - 2;
    };


    /*
     * Return true if the value of this BigNumber is NaN, otherwise return false.
     */
    P.isNaN = function () {
        return !this.s;
    };


    /*
     * Return true if the value of this BigNumber is negative, otherwise return false.
     */
    P.isNegative = function () {
        return this.s < 0;
    };


    /*
     * Return true if the value of this BigNumber is positive, otherwise return false.
     */
    P.isPositive = function () {
        return this.s > 0;
    };


    /*
     * Return true if the value of this BigNumber is 0 or -0, otherwise return false.
     */
    P.isZero = function () {
        return !!this.c && this.c[0] == 0;
    };


    /*
     * Return true if the value of this BigNumber is less than the value of BigNumber(y, b),
     * otherwise return false.
     */
    P.isLessThan = P.lt = function ( y, b ) {
        return compare( this, new BigNumber( y, b ) ) < 0;
    };


    /*
     * Return true if the value of this BigNumber is less than or equal to the value of
     * BigNumber(y, b), otherwise return false.
     */
    P.isLessThanOrEqualTo = P.lte = function ( y, b ) {
        return ( b = compare( this, new BigNumber( y, b ) ) ) === -1 || b === 0;
    };


    /*
     *  n - 0 = n
     *  n - N = N
     *  n - I = -I
     *  0 - n = -n
     *  0 - 0 = 0
     *  0 - N = N
     *  0 - I = -I
     *  N - n = N
     *  N - 0 = N
     *  N - N = N
     *  N - I = N
     *  I - n = I
     *  I - 0 = I
     *  I - N = N
     *  I - I = N
     *
     * Return a new BigNumber whose value is the value of this BigNumber minus the value of
     * BigNumber(y, b).
     */
    P.minus = function ( y, b ) {
        var i, j, t, xLTy,
            x = this,
            a = x.s;

        y = new BigNumber( y, b );
        b = y.s;

        // Either NaN?
        if ( !a || !b ) return new BigNumber(NaN);

        // Signs differ?
        if ( a != b ) {
            y.s = -b;
            return x.plus(y);
        }

        var xe = x.e / LOG_BASE,
            ye = y.e / LOG_BASE,
            xc = x.c,
            yc = y.c;

        if ( !xe || !ye ) {

            // Either Infinity?
            if ( !xc || !yc ) return xc ? ( y.s = -b, y ) : new BigNumber( yc ? x : NaN );

            // Either zero?
            if ( !xc[0] || !yc[0] ) {

                // Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
                return yc[0] ? ( y.s = -b, y ) : new BigNumber( xc[0] ? x :

                  // IEEE 754 (2008) 6.3: n - n = -0 when rounding to -Infinity
                  ROUNDING_MODE == 3 ? -0 : 0 );
            }
        }

        xe = bitFloor(xe);
        ye = bitFloor(ye);
        xc = xc.slice();

        // Determine which is the bigger number.
        if ( a = xe - ye ) {

            if ( xLTy = a < 0 ) {
                a = -a;
                t = xc;
            } else {
                ye = xe;
                t = yc;
            }

            t.reverse();

            // Prepend zeros to equalise exponents.
            for ( b = a; b--; t.push(0) );
            t.reverse();
        } else {

            // Exponents equal. Check digit by digit.
            j = ( xLTy = ( a = xc.length ) < ( b = yc.length ) ) ? a : b;

            for ( a = b = 0; b < j; b++ ) {

                if ( xc[b] != yc[b] ) {
                    xLTy = xc[b] < yc[b];
                    break;
                }
            }
        }

        // x < y? Point xc to the array of the bigger number.
        if (xLTy) t = xc, xc = yc, yc = t, y.s = -y.s;

        b = ( j = yc.length ) - ( i = xc.length );

        // Append zeros to xc if shorter.
        // No need to add zeros to yc if shorter as subtract only needs to start at yc.length.
        if ( b > 0 ) for ( ; b--; xc[i++] = 0 );
        b = BASE - 1;

        // Subtract yc from xc.
        for ( ; j > a; ) {

            if ( xc[--j] < yc[j] ) {
                for ( i = j; i && !xc[--i]; xc[i] = b );
                --xc[i];
                xc[j] += BASE;
            }

            xc[j] -= yc[j];
        }

        // Remove leading zeros and adjust exponent accordingly.
        for ( ; xc[0] == 0; xc.splice(0, 1), --ye );

        // Zero?
        if ( !xc[0] ) {

            // Following IEEE 754 (2008) 6.3,
            // n - n = +0  but  n - n = -0  when rounding towards -Infinity.
            y.s = ROUNDING_MODE == 3 ? -1 : 1;
            y.c = [ y.e = 0 ];
            return y;
        }

        // No need to check for Infinity as +x - +y != Infinity && -x - -y != Infinity
        // for finite x and y.
        return normalise( y, xc, ye );
    };


    /*
     *   n % 0 =  N
     *   n % N =  N
     *   n % I =  n
     *   0 % n =  0
     *  -0 % n = -0
     *   0 % 0 =  N
     *   0 % N =  N
     *   0 % I =  0
     *   N % n =  N
     *   N % 0 =  N
     *   N % N =  N
     *   N % I =  N
     *   I % n =  N
     *   I % 0 =  N
     *   I % N =  N
     *   I % I =  N
     *
     * Return a new BigNumber whose value is the value of this BigNumber modulo the value of
     * BigNumber(y, b). The result depends on the value of MODULO_MODE.
     */
    P.modulo = P.mod = function ( y, b ) {
        var q, s,
            x = this;

        y = new BigNumber( y, b );

        // Return NaN if x is Infinity or NaN, or y is NaN or zero.
        if ( !x.c || !y.s || y.c && !y.c[0] ) {
            return new BigNumber(NaN);

        // Return x if y is Infinity or x is zero.
        } else if ( !y.c || x.c && !x.c[0] ) {
            return new BigNumber(x);
        }

        if ( MODULO_MODE == 9 ) {

            // Euclidian division: q = sign(y) * floor(x / abs(y))
            // r = x - qy    where  0 <= r < abs(y)
            s = y.s;
            y.s = 1;
            q = div( x, y, 0, 3 );
            y.s = s;
            q.s *= s;
        } else {
            q = div( x, y, 0, MODULO_MODE );
        }

        return x.minus( q.times(y) );
    };


    /*
     *  n * 0 = 0
     *  n * N = N
     *  n * I = I
     *  0 * n = 0
     *  0 * 0 = 0
     *  0 * N = N
     *  0 * I = N
     *  N * n = N
     *  N * 0 = N
     *  N * N = N
     *  N * I = N
     *  I * n = I
     *  I * 0 = N
     *  I * N = N
     *  I * I = I
     *
     * Return a new BigNumber whose value is the value of this BigNumber multiplied by the value
     * of BigNumber(y, b).
     */
    P.multipliedBy = P.times = function ( y, b ) {
        var c, e, i, j, k, m, xcL, xlo, xhi, ycL, ylo, yhi, zc,
            base, sqrtBase,
            x = this,
            xc = x.c,
            yc = ( y = new BigNumber( y, b ) ).c;

        // Either NaN, ±Infinity or ±0?
        if ( !xc || !yc || !xc[0] || !yc[0] ) {

            // Return NaN if either is NaN, or one is 0 and the other is Infinity.
            if ( !x.s || !y.s || xc && !xc[0] && !yc || yc && !yc[0] && !xc ) {
                y.c = y.e = y.s = null;
            } else {
                y.s *= x.s;

                // Return ±Infinity if either is ±Infinity.
                if ( !xc || !yc ) {
                    y.c = y.e = null;

                // Return ±0 if either is ±0.
                } else {
                    y.c = [0];
                    y.e = 0;
                }
            }

            return y;
        }

        e = bitFloor( x.e / LOG_BASE ) + bitFloor( y.e / LOG_BASE );
        y.s *= x.s;
        xcL = xc.length;
        ycL = yc.length;

        // Ensure xc points to longer array and xcL to its length.
        if ( xcL < ycL ) zc = xc, xc = yc, yc = zc, i = xcL, xcL = ycL, ycL = i;

        // Initialise the result array with zeros.
        for ( i = xcL + ycL, zc = []; i--; zc.push(0) );

        base = BASE;
        sqrtBase = SQRT_BASE;

        for ( i = ycL; --i >= 0; ) {
            c = 0;
            ylo = yc[i] % sqrtBase;
            yhi = yc[i] / sqrtBase | 0;

            for ( k = xcL, j = i + k; j > i; ) {
                xlo = xc[--k] % sqrtBase;
                xhi = xc[k] / sqrtBase | 0;
                m = yhi * xlo + xhi * ylo;
                xlo = ylo * xlo + ( ( m % sqrtBase ) * sqrtBase ) + zc[j] + c;
                c = ( xlo / base | 0 ) + ( m / sqrtBase | 0 ) + yhi * xhi;
                zc[j--] = xlo % base;
            }

            zc[j] = c;
        }

        if (c) {
            ++e;
        } else {
            zc.splice(0, 1);
        }

        return normalise( y, zc, e );
    };


    /*
     * Return a new BigNumber whose value is the value of this BigNumber negated,
     * i.e. multiplied by -1.
     */
    P.negated = function () {
        var x = new BigNumber(this);
        x.s = -x.s || null;
        return x;
    };


    /*
     *  n + 0 = n
     *  n + N = N
     *  n + I = I
     *  0 + n = n
     *  0 + 0 = 0
     *  0 + N = N
     *  0 + I = I
     *  N + n = N
     *  N + 0 = N
     *  N + N = N
     *  N + I = N
     *  I + n = I
     *  I + 0 = I
     *  I + N = N
     *  I + I = I
     *
     * Return a new BigNumber whose value is the value of this BigNumber plus the value of
     * BigNumber(y, b).
     */
    P.plus = function ( y, b ) {
        var t,
            x = this,
            a = x.s;

        y = new BigNumber( y, b );
        b = y.s;

        // Either NaN?
        if ( !a || !b ) return new BigNumber(NaN);

        // Signs differ?
         if ( a != b ) {
            y.s = -b;
            return x.minus(y);
        }

        var xe = x.e / LOG_BASE,
            ye = y.e / LOG_BASE,
            xc = x.c,
            yc = y.c;

        if ( !xe || !ye ) {

            // Return ±Infinity if either ±Infinity.
            if ( !xc || !yc ) return new BigNumber( a / 0 );

            // Either zero?
            // Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
            if ( !xc[0] || !yc[0] ) return yc[0] ? y : new BigNumber( xc[0] ? x : a * 0 );
        }

        xe = bitFloor(xe);
        ye = bitFloor(ye);
        xc = xc.slice();

        // Prepend zeros to equalise exponents. Faster to use reverse then do unshifts.
        if ( a = xe - ye ) {
            if ( a > 0 ) {
                ye = xe;
                t = yc;
            } else {
                a = -a;
                t = xc;
            }

            t.reverse();
            for ( ; a--; t.push(0) );
            t.reverse();
        }

        a = xc.length;
        b = yc.length;

        // Point xc to the longer array, and b to the shorter length.
        if ( a - b < 0 ) t = yc, yc = xc, xc = t, b = a;

        // Only start adding at yc.length - 1 as the further digits of xc can be ignored.
        for ( a = 0; b; ) {
            a = ( xc[--b] = xc[b] + yc[b] + a ) / BASE | 0;
            xc[b] = BASE === xc[b] ? 0 : xc[b] % BASE;
        }

        if (a) {
            xc = [a].concat(xc);
            ++ye;
        }

        // No need to check for zero, as +x + +y != 0 && -x + -y != 0
        // ye = MAX_EXP + 1 possible
        return normalise( y, xc, ye );
    };


    /*
     * If sd is undefined or null or true or false, return the number of significant digits of
     * the value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN.
     * If sd is true include integer-part trailing zeros in the count.
     *
     * Otherwise, if sd is a number, return a new BigNumber whose value is the value of this
     * BigNumber rounded to a maximum of sd significant digits using rounding mode rm, or
     * ROUNDING_MODE if rm is omitted.
     *
     * sd {number|boolean} number: significant digits: integer, 1 to MAX inclusive.
     *                     boolean: whether to count integer-part trailing zeros: true or false.
     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
     *
     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {sd|rm}'
     */
    P.precision = P.sd = function ( sd, rm ) {
        var c, n, v,
            x = this;

        if ( sd != null && sd !== !!sd ) {
            intCheck( sd, 1, MAX );
            if ( rm == null ) rm = ROUNDING_MODE;
            else intCheck( rm, 0, 8 );

            return round( new BigNumber(x), sd, rm );
        }

        if ( !( c = x.c ) ) return null;
        v = c.length - 1;
        n = v * LOG_BASE + 1;

        if ( v = c[v] ) {

            // Subtract the number of trailing zeros of the last element.
            for ( ; v % 10 == 0; v /= 10, n-- );

            // Add the number of digits of the first element.
            for ( v = c[0]; v >= 10; v /= 10, n++ );
        }

        if ( sd && x.e + 1 > n ) n = x.e + 1;

        return n;
    };


    /*
     * Return a new BigNumber whose value is the value of this BigNumber shifted by k places
     * (powers of 10). Shift to the right if n > 0, and to the left if n < 0.
     *
     * k {number} Integer, -MAX_SAFE_INTEGER to MAX_SAFE_INTEGER inclusive.
     *
     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {k}'
     */
    P.shiftedBy = function (k) {
        intCheck( k, -MAX_SAFE_INTEGER, MAX_SAFE_INTEGER );
        return this.times( '1e' + k );
    };


    /*
     *  sqrt(-n) =  N
     *  sqrt( N) =  N
     *  sqrt(-I) =  N
     *  sqrt( I) =  I
     *  sqrt( 0) =  0
     *  sqrt(-0) = -0
     *
     * Return a new BigNumber whose value is the square root of the value of this BigNumber,
     * rounded according to DECIMAL_PLACES and ROUNDING_MODE.
     */
    P.squareRoot = P.sqrt = function () {
        var m, n, r, rep, t,
            x = this,
            c = x.c,
            s = x.s,
            e = x.e,
            dp = DECIMAL_PLACES + 4,
            half = new BigNumber('0.5');

        // Negative/NaN/Infinity/zero?
        if ( s !== 1 || !c || !c[0] ) {
            return new BigNumber( !s || s < 0 && ( !c || c[0] ) ? NaN : c ? x : 1 / 0 );
        }

        // Initial estimate.
        s = Math.sqrt( +x );

        // Math.sqrt underflow/overflow?
        // Pass x to Math.sqrt as integer, then adjust the exponent of the result.
        if ( s == 0 || s == 1 / 0 ) {
            n = coeffToString(c);
            if ( ( n.length + e ) % 2 == 0 ) n += '0';
            s = Math.sqrt(n);
            e = bitFloor( ( e + 1 ) / 2 ) - ( e < 0 || e % 2 );

            if ( s == 1 / 0 ) {
                n = '1e' + e;
            } else {
                n = s.toExponential();
                n = n.slice( 0, n.indexOf('e') + 1 ) + e;
            }

            r = new BigNumber(n);
        } else {
            r = new BigNumber( s + '' );
        }

        // Check for zero.
        // r could be zero if MIN_EXP is changed after the this value was created.
        // This would cause a division by zero (x/t) and hence Infinity below, which would cause
        // coeffToString to throw.
        if ( r.c[0] ) {
            e = r.e;
            s = e + dp;
            if ( s < 3 ) s = 0;

            // Newton-Raphson iteration.
            for ( ; ; ) {
                t = r;
                r = half.times( t.plus( div( x, t, dp, 1 ) ) );

                if ( coeffToString( t.c   ).slice( 0, s ) === ( n =
                     coeffToString( r.c ) ).slice( 0, s ) ) {

                    // The exponent of r may here be one less than the final result exponent,
                    // e.g 0.0009999 (e-4) --> 0.001 (e-3), so adjust s so the rounding digits
                    // are indexed correctly.
                    if ( r.e < e ) --s;
                    n = n.slice( s - 3, s + 1 );

                    // The 4th rounding digit may be in error by -1 so if the 4 rounding digits
                    // are 9999 or 4999 (i.e. approaching a rounding boundary) continue the
                    // iteration.
                    if ( n == '9999' || !rep && n == '4999' ) {

                        // On the first iteration only, check to see if rounding up gives the
                        // exact result as the nines may infinitely repeat.
                        if ( !rep ) {
                            round( t, t.e + DECIMAL_PLACES + 2, 0 );

                            if ( t.times(t).eq(x) ) {
                                r = t;
                                break;
                            }
                        }

                        dp += 4;
                        s += 4;
                        rep = 1;
                    } else {

                        // If rounding digits are null, 0{0,4} or 50{0,3}, check for exact
                        // result. If not, then there are further digits and m will be truthy.
                        if ( !+n || !+n.slice(1) && n.charAt(0) == '5' ) {

                            // Truncate to the first rounding digit.
                            round( r, r.e + DECIMAL_PLACES + 2, 1 );
                            m = !r.times(r).eq(x);
                        }

                        break;
                    }
                }
            }
        }

        return round( r, r.e + DECIMAL_PLACES + 1, ROUNDING_MODE, m );
    };


    /*
     * Return a string representing the value of this BigNumber in exponential notation and
     * rounded using ROUNDING_MODE to dp fixed decimal places.
     *
     * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
     *
     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
     */
    P.toExponential = function ( dp, rm ) {
        if ( dp != null ) {
            intCheck( dp, 0, MAX );
            dp++;
        }
        return format( this, dp, rm, 1 );
    };


    /*
     * Return a string representing the value of this BigNumber in fixed-point notation rounding
     * to dp fixed decimal places using rounding mode rm, or ROUNDING_MODE if rm is omitted.
     *
     * Note: as with JavaScript's number type, (-0).toFixed(0) is '0',
     * but e.g. (-0.00001).toFixed(0) is '-0'.
     *
     * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
     *
     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
     */
    P.toFixed = function ( dp, rm ) {
        if ( dp != null ) {
            intCheck( dp, 0, MAX );
            dp = dp + this.e + 1;
        }
        return format( this, dp, rm );
    };


    /*
     * Return a string representing the value of this BigNumber in fixed-point notation rounded
     * using rm or ROUNDING_MODE to dp decimal places, and formatted according to the properties
     * of the FORMAT object (see BigNumber.set).
     *
     * FORMAT = {
     *      decimalSeparator : '.',
     *      groupSeparator : ',',
     *      groupSize : 3,
     *      secondaryGroupSize : 0,
     *      fractionGroupSeparator : '\xA0',    // non-breaking space
     *      fractionGroupSize : 0
     * };
     *
     * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
     *
     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
     */
    P.toFormat = function ( dp, rm ) {
        var str = this.toFixed( dp, rm );

        if ( this.c ) {
            var i,
                arr = str.split('.'),
                g1 = +FORMAT.groupSize,
                g2 = +FORMAT.secondaryGroupSize,
                groupSeparator = FORMAT.groupSeparator,
                intPart = arr[0],
                fractionPart = arr[1],
                isNeg = this.s < 0,
                intDigits = isNeg ? intPart.slice(1) : intPart,
                len = intDigits.length;

            if (g2) i = g1, g1 = g2, g2 = i, len -= i;

            if ( g1 > 0 && len > 0 ) {
                i = len % g1 || g1;
                intPart = intDigits.substr( 0, i );

                for ( ; i < len; i += g1 ) {
                    intPart += groupSeparator + intDigits.substr( i, g1 );
                }

                if ( g2 > 0 ) intPart += groupSeparator + intDigits.slice(i);
                if (isNeg) intPart = '-' + intPart;
            }

            str = fractionPart
              ? intPart + FORMAT.decimalSeparator + ( ( g2 = +FORMAT.fractionGroupSize )
                ? fractionPart.replace( new RegExp( '\\d{' + g2 + '}\\B', 'g' ),
                  '$&' + FORMAT.fractionGroupSeparator )
                : fractionPart )
              : intPart;
        }

        return str;
    };


    /*
     * Return a string array representing the value of this BigNumber as a simple fraction with
     * an integer numerator and an integer denominator. The denominator will be a positive
     * non-zero value less than or equal to the specified maximum denominator. If a maximum
     * denominator is not specified, the denominator will be the lowest value necessary to
     * represent the number exactly.
     *
     * [md] {number|string|BigNumber} Integer >= 1 and < Infinity. The maximum denominator.
     *
     * '[BigNumber Error] Argument {not an integer|out of range} : {md}'
     */
    P.toFraction = function (md) {
        var arr, d, d0, d1, d2, e, exp, n, n0, n1, q, s,
            x = this,
            xc = x.c;

        if ( md != null ) {
            n = new BigNumber(md);

            if ( !n.isInteger() || n.lt(ONE) ) {
                throw Error
                  ( bignumberError + 'Argument ' +
                    ( n.isInteger() ? 'out of range: ' : 'not an integer: ' ) + md );
            }
        }

        if ( !xc ) return x.toString();

        d = new BigNumber(ONE);
        n1 = d0 = new BigNumber(ONE);
        d1 = n0 = new BigNumber(ONE);
        s = coeffToString(xc);

        // Determine initial denominator.
        // d is a power of 10 and the minimum max denominator that specifies the value exactly.
        e = d.e = s.length - x.e - 1;
        d.c[0] = POWS_TEN[ ( exp = e % LOG_BASE ) < 0 ? LOG_BASE + exp : exp ];
        md = !md || n.comparedTo(d) > 0 ? ( e > 0 ? d : n1 ) : n;

        exp = MAX_EXP;
        MAX_EXP = 1 / 0;
        n = new BigNumber(s);

        // n0 = d1 = 0
        n0.c[0] = 0;

        for ( ; ; )  {
            q = div( n, d, 0, 1 );
            d2 = d0.plus( q.times(d1) );
            if ( d2.comparedTo(md) == 1 ) break;
            d0 = d1;
            d1 = d2;
            n1 = n0.plus( q.times( d2 = n1 ) );
            n0 = d2;
            d = n.minus( q.times( d2 = d ) );
            n = d2;
        }

        d2 = div( md.minus(d0), d1, 0, 1 );
        n0 = n0.plus( d2.times(n1) );
        d0 = d0.plus( d2.times(d1) );
        n0.s = n1.s = x.s;
        e *= 2;

        // Determine which fraction is closer to x, n0/d0 or n1/d1
        arr = div( n1, d1, e, ROUNDING_MODE ).minus(x).abs().comparedTo(
              div( n0, d0, e, ROUNDING_MODE ).minus(x).abs() ) < 1
                ? [ n1.toString(), d1.toString() ]
                : [ n0.toString(), d0.toString() ];

        MAX_EXP = exp;
        return arr;
    };


    /*
     * Return the value of this BigNumber converted to a number primitive.
     */
    P.toNumber = function () {
        return +this;
    };


    /*
     * Return a BigNumber whose value is the value of this BigNumber exponentiated by n.
     *
     * If m is present, return the result modulo m.
     * If n is negative round according to DECIMAL_PLACES and ROUNDING_MODE.
     * If POW_PRECISION is non-zero and m is not present, round to POW_PRECISION using ROUNDING_MODE.
     *
     * The modular power operation works efficiently when x, n, and m are positive integers,
     * otherwise it is equivalent to calculating x.exponentiatedBy(n).modulo(m) with a POW_PRECISION of 0.
     *
     * n {number} Integer, -MAX_SAFE_INTEGER to MAX_SAFE_INTEGER inclusive.
     * [m] {number|string|BigNumber} The modulus.
     *
     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {n}'
     *
     * Performs 54 loop iterations for n of 9007199254740991.
     */
    P.exponentiatedBy = P.pow = function ( n, m ) {
        var i, k, y, z,
            x = this;

        intCheck( n, -MAX_SAFE_INTEGER, MAX_SAFE_INTEGER );
        if ( m != null ) m = new BigNumber(m);

        if (m) {
            if ( n > 1 && x.gt(ONE) && x.isInteger() && m.gt(ONE) && m.isInteger() ) {
                x = x.mod(m);
            } else {
                z = m;

                // Nullify m so only a single mod operation is performed at the end.
                m = null;
            }
        } else if (POW_PRECISION) {

            // Truncating each coefficient array to a length of k after each multiplication
            // equates to truncating significant digits to POW_PRECISION + [28, 41],
            // i.e. there will be a minimum of 28 guard digits retained.
            //k = mathceil( POW_PRECISION / LOG_BASE + 1.5 );   // gives [9, 21] guard digits.
            k = mathceil( POW_PRECISION / LOG_BASE + 2 );
        }

        y = new BigNumber(ONE);

        for ( i = mathfloor( n < 0 ? -n : n ); ; ) {
            if ( i % 2 ) {
                y = y.times(x);
                if ( !y.c ) break;
                if (k) {
                    if ( y.c.length > k ) y.c.length = k;
                } else if (m) {
                    y = y.mod(m);
                }
            }

            i = mathfloor( i / 2 );
            if ( !i ) break;
            x = x.times(x);
            if (k) {
                if ( x.c && x.c.length > k ) x.c.length = k;
            } else if (m) {
                x = x.mod(m);
            }
        }

        if (m) return y;
        if ( n < 0 ) y = ONE.div(y);

        return z ? y.mod(z) : k ? round( y, POW_PRECISION, ROUNDING_MODE ) : y;
    };


    /*
     * Return a string representing the value of this BigNumber rounded to sd significant digits
     * using rounding mode rm or ROUNDING_MODE. If sd is less than the number of digits
     * necessary to represent the integer part of the value in fixed-point notation, then use
     * exponential notation.
     *
     * [sd] {number} Significant digits. Integer, 1 to MAX inclusive.
     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
     *
     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {sd|rm}'
     */
    P.toPrecision = function ( sd, rm ) {
        if ( sd != null ) intCheck( sd, 1, MAX );
        return format( this, sd, rm, 2 );
    };


    /*
     * Return a string representing the value of this BigNumber in base b, or base 10 if b is
     * omitted. If a base is specified, including base 10, round according to DECIMAL_PLACES and
     * ROUNDING_MODE. If a base is not specified, and this BigNumber has a positive exponent
     * that is equal to or greater than TO_EXP_POS, or a negative exponent equal to or less than
     * TO_EXP_NEG, return exponential notation.
     *
     * [b] {number} Integer, 2 to ALPHABET.length inclusive.
     *
     * '[BigNumber Error] Base {not a primitive number|not an integer|out of range}: {b}'
     */
    P.toString = function (b) {
        var str,
            n = this,
            s = n.s,
            e = n.e;

        // Infinity or NaN?
        if ( e === null ) {

            if (s) {
                str = 'Infinity';
                if ( s < 0 ) str = '-' + str;
            } else {
                str = 'NaN';
            }
        } else {
            str = coeffToString( n.c );

            if ( b == null ) {
                str = e <= TO_EXP_NEG || e >= TO_EXP_POS
                  ? toExponential( str, e )
                  : toFixedPoint( str, e, '0' );
            } else {
                intCheck( b, 2, ALPHABET.length, 'Base' );
                str = convertBase( toFixedPoint( str, e, '0' ), 10, b, s, true );
            }

            if ( s < 0 && n.c[0] ) str = '-' + str;
        }

        return str;
    };


    /*
     * Return as toString, but do not accept a base argument, and include the minus sign for
     * negative zero.
     */
    P.valueOf = P.toJSON = function () {
        var str,
            n = this,
            e = n.e;

        if ( e === null ) return n.toString();

        str = coeffToString( n.c );

        str = e <= TO_EXP_NEG || e >= TO_EXP_POS
            ? toExponential( str, e )
            : toFixedPoint( str, e, '0' );

        return n.s < 0 ? '-' + str : str;
    };


    P._isBigNumber = true;

    if ( configObject != null ) BigNumber.set(configObject);

    return BigNumber;
}


// PRIVATE HELPER FUNCTIONS


function bitFloor(n) {
    var i = n | 0;
    return n > 0 || n === i ? i : i - 1;
}


// Return a coefficient array as a string of base 10 digits.
function coeffToString(a) {
    var s, z,
        i = 1,
        j = a.length,
        r = a[0] + '';

    for ( ; i < j; ) {
        s = a[i++] + '';
        z = LOG_BASE - s.length;
        for ( ; z--; s = '0' + s );
        r += s;
    }

    // Determine trailing zeros.
    for ( j = r.length; r.charCodeAt(--j) === 48; );
    return r.slice( 0, j + 1 || 1 );
}


// Compare the value of BigNumbers x and y.
function compare( x, y ) {
    var a, b,
        xc = x.c,
        yc = y.c,
        i = x.s,
        j = y.s,
        k = x.e,
        l = y.e;

    // Either NaN?
    if ( !i || !j ) return null;

    a = xc && !xc[0];
    b = yc && !yc[0];

    // Either zero?
    if ( a || b ) return a ? b ? 0 : -j : i;

    // Signs differ?
    if ( i != j ) return i;

    a = i < 0;
    b = k == l;

    // Either Infinity?
    if ( !xc || !yc ) return b ? 0 : !xc ^ a ? 1 : -1;

    // Compare exponents.
    if ( !b ) return k > l ^ a ? 1 : -1;

    j = ( k = xc.length ) < ( l = yc.length ) ? k : l;

    // Compare digit by digit.
    for ( i = 0; i < j; i++ ) if ( xc[i] != yc[i] ) return xc[i] > yc[i] ^ a ? 1 : -1;

    // Compare lengths.
    return k == l ? 0 : k > l ^ a ? 1 : -1;
}


/*
 * Check that n is a primitive number, an integer, and in range, otherwise throw.
 */
function intCheck( n, min, max, name ) {
    if ( n < min || n > max || n !== ( n < 0 ? mathceil(n) : mathfloor(n) ) ) {
        throw Error
          ( bignumberError + ( name || 'Argument' ) + ( typeof n == 'number'
              ? n < min || n > max ? ' out of range: ' : ' not an integer: '
              : ' not a primitive number: ' ) + n );
    }
}


function isArray(obj) {
    return Object.prototype.toString.call(obj) == '[object Array]';
}


function toExponential( str, e ) {
    return ( str.length > 1 ? str.charAt(0) + '.' + str.slice(1) : str ) +
      ( e < 0 ? 'e' : 'e+' ) + e;
}


function toFixedPoint( str, e, z ) {
    var len, zs;

    // Negative exponent?
    if ( e < 0 ) {

        // Prepend zeros.
        for ( zs = z + '.'; ++e; zs += z );
        str = zs + str;

    // Positive exponent
    } else {
        len = str.length;

        // Append zeros.
        if ( ++e > len ) {
            for ( zs = z, e -= len; --e; zs += z );
            str += zs;
        } else if ( e < len ) {
            str = str.slice( 0, e ) + '.' + str.slice(e);
        }
    }

    return str;
}


// EXPORT


BigNumber = clone();
BigNumber['default'] = BigNumber.BigNumber = BigNumber;

export default BigNumber;
